Final answer:
To analyze the limit of the function f(x) = (1 - x - 2x² - x³)/(x² + 1), substitute the real number, a, into the function and simplify.
Step-by-step explanation:
The given function is f(x) = (1 - x - 2x² - x³)/(x² + 1). To analyze the limit of this function, we need to find the behavior of f(x) as x approaches a certain value. Let's consider the limit as x approaches a real number, say a. We can evaluate this limit by substituting a into the function and simplifying:
limx→a f(x) = limx→a [(1 - x - 2x² - x³)/(x² + 1)] = [(1 - a - 2a² - a³)/(a² + 1)].
This is the limit of the function f(x) as x approaches a real number, a.